Use the table to answer the question.
Cups of Flour Loaves of Bread
1 12
2 1
3 112
4 2
A bakery is making loaves of French bread. The recipe calls for 2 cups of flour per loaf of bread. The data table shows how much flour the bakery needs depending on the number of loaves it intends to make. At which ratio in the data table does the constant of proportionality appear? Write your answer as an ordered pair inside the parentheses provided.
(1 point)
The constant of proportionality appears in the ratio $\boxed{(2,1)}$.
The constant of proportionality appears at the ratio (2, 1) in the data table.
To find the constant of proportionality in the data table, we need to look for a ratio where the number of cups of flour is directly proportional to the number of loaves of bread.
Let's calculate the ratios for each data point:
(1 cup of flour, 12 loaves of bread) - ratio = 12/1 = 12
(2 cups of flour, 1 loaf of bread) - ratio = 1/2 = 0.5
(3 cups of flour, 112 loaves of bread) - ratio = 112/3 ≈ 37.33
(4 cups of flour, 2 loaves of bread) - ratio = 2/4 = 0.5
The ratio where the constant of proportionality appears is the one that has the same value for all data points. From the calculations above, we can see that the ratio 0.5 appears twice, for the data points (2 cups of flour, 1 loaf of bread) and (4 cups of flour, 2 loaves of bread).
Therefore, the constant of proportionality in this data table is a ratio of 0.5. It can be written as an ordered pair (cups of flour, loaves of bread) inside the parentheses: (2, 1).